Mathematics, 27.09.2019 12:00 moldybubblegum11

Identify the graph of 2x^2+2y^=9 for theta=30º and write and equation of the translated or rotated graph in general form.

Identify the graph of 2x^2+2y^=9 for theta=30º and write and equation of the translated or rotated g

Answers: 1

Show answers

Answers

Answer from: maddie4985

The answer is circle; (x')² + (y')² - 4 = 0

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy² + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* 2x² + 2y² = 8

∵ A = 2 , B = 0 , C = 2

∴ B² - 4AC = (0) - 4(2)(2) = -16 < 0

∵ B² - 4AC < 0

∴ it will be either a circle or an ellipse

* Lets use this note to chose the correct figure

- If A and C are equal and nonzero and have the same sign,

then the graph is a circle.

- If A and C are nonzero, have the same sign, and are not equal

to each other, then the graph is an ellipse.

∵ A = 2 and C = 2

∴ The graph is a circle.

∵ D and E = 0

∴ The center of the circle is the origin (0 , 0)

∵ Ф = 30°

∴ The point (x , y) will be (x' , y')

- Where x = x'cosФ - y' sinФ and y = x'sinФ + y'cosФ

∴ x = x'cos(30°) - y'sin(30°)

∴ y = x'sin(30°) + y'cos(30°)

∴ x = (√3/2)x' - (1/2)y' and y = (1/2)x' + (√3/2)y'

∴ $x=\frac{\sqrt{3}x'-y'}{2}$

∴ $y=\frac{x'+\sqrt{3}y'}{2}$

* Lets substitute x and y in the first equation

∴ $2(\frac{\sqrt{3}x'-y'}{2})^{2}+2(\frac{x'+\sqrt{3}y'}{2})^{2}=8$

* Use the foil method

∴ $2(\frac{3x'^{2}-2\sqrt{3}x'y'+y'^{2}}{4})+2(\frac{x'^{2}+2\sqrt{3}x'y'+3y'^{2}}{4})=8$

* Open the brackets

∴ $\frac{3x'^{2}-2\sqrt{3}x'y'+y'^{2}+x'^{2}+2\sqrt{3}x'y'+3y'^{2}}{2}=8$

* Collect the like terms

∴ $\frac{4x'^{2}+4y'^{2}}{2}=8$

* Simplify the fraction

∴ 2(x')² + 2(y')²= 8

* Divide each side by 2

∴ (x')² + (y')² = 4

∴ The equation of the circle is (x')² + (y')² = 4

* The general equation of the circle is (x')² + (y')² - 4 = 0

after rotation 30° about the origin

* Look to the graph

- The blue circle for the equation 2x² + 2y² = 8

- The blue circle for equation (x')² + (y')² - 4 = 0

* That is because the two circles have same centers and radii

- The green line is x' and the purple line is y'

Identify the graph of 2x^2+2y^=9 for theta=30º and write and equation of the translated or rotated g

Answer from: Quest

B. because the 7 represents "seven times", x represents "a number", 12 represents "plus twelve", and -4 represents "minus four"
Which of the following best describes an algebraic expression 7 (x+ 12) -4

Which of the following best describes an algebraic expression 7 (x+ 12) -4

Answer from: Quest

given : the shape of his satellite can be modeled by where x and y are modeled in inches.

now,the given equation is a equation of parabola.

here, coefficient of x is positive, hence the parabola opens rightwards.

on comparing this equation with standard equation , we get

in standard equation, coordinates of focus=(0,m)

thus for given equation coordinates of focus=(0,1.5)

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:00, jamiecoolgal8697

Question: what is the value of x 4x-2= (-7) +5x. it would be greatly appreciated if someone could actually explain to me step by step

Answers: 2

continue

Mathematics, 21.06.2019 17:20, Ndow2

Which functions shave a maximum and are transformed to the left and down of the parent function ,check all that apply f(x) = x2? p(x) =14 (x+7)2 + 1

Answers: 3

continue

Mathematics, 21.06.2019 19:50, gomez36495983

Raj encoded a secret phrase using matrix multiplication. using a = 1, b = 2, c = 3, and so on, he multiplied the clear text code for each letter by the matrix to get a matrix that represents the encoded text. the matrix representing the encoded text is . what is the secret phrase? determine the location of spaces after you decode the text. yummy is the corn the tomato is red the corn is yummy red is the tomato

Answers: 2

continue

Mathematics, 21.06.2019 22:10, markayla101326

In which direction does the left side of the graph of this function point? f(x) = 3x3 - x2 + 4x - 2

Answers: 2

continue

You know the right answer?

Identify the graph of 2x^2+2y^=9 for theta=30º and write and equation of the translated or rotated g...